玻璃纤维增强树脂基复合材料疲劳行为研究
|
摘要
玻璃纤维增强树脂基复合材料在航空、汽车、船舶以及民用工业都得到了广泛应用,虽然玻璃纤维增强树脂基复合材料的疲劳现象无处不在,但现在还没有办法从疲劳现象出发对其疲劳本质作出恰如其分描述,同时也没有对其进行疲劳寿命分析的通用方法。本文对玻璃纤维增强复合材料的疲劳行为进行了系统的实验和理论研究。
论文首先回顾了纤维增强复合材料疲劳行为研究领域已经取得的研究成果,并对这些成果进行了分析和论述,通过实验数据的计算比较,给出了各种分析模型的适应性和解决实际问题的符合程度。
论文完成了6种层合板162个有效的玻璃纤维增强树脂基复合材料层合板试验件的测试,其中50个试件用于静强度测试,112个试件用于疲劳性能测试。获得了比较系统的玻璃纤维增强复合材料层合板的疲劳性能数据。给出了同种试件在不同的加载比下的刚度降曲线,以及不同种类试件在相同加载比下的刚度降曲线,并从材料内部微观损伤扩展机理的角度解释了刚度随损伤单调下降原因。在疲劳试验的基础上对玻璃纤维增强复合材料层合板的疲劳行为开展了理论研究:给出了定义玻璃纤维增强复合材料层合板在轴向应力作用下的状态函数,提出了一个由0°和90°单向板的S—N曲线来获得任意偏角层合板的S—N曲线的疲劳寿命模型;基于玻璃纤维增强复合材料层合板的疲劳破坏机理,提出了一个由0°和90°单向板的S—N曲线来获得任意铺层层合板S—N曲线的模型;提出了一个描述层合板刚度退化的模型,该模型可以很好地描述玻璃纤维增强复合材料层合板的刚度退化规律。
研究结果表明:论文中提出的理论分析模型和实验结果吻合的很好。本文所获得的实验结果可直接用于玻璃纤维增强树脂基复合材料结构的设计,所提出的理论分析模型可用于任意铺层的玻璃纤维增强复合材料层合板结构的分析计算。
Glass Fiber Reinforced Polymer (GFRP) has been widely used in the fields of aeronautics, automobile, shipping and civil industry. Although the fatigue problem of the GFRP were encountered everywhere, the fatigue mechanism could not be essentially described based on its fatigue phenomena, and there was no general method for the fatigue life’s prediction. In this paper, the fatigue behaviors of GFRP laminates were systematically researched by theoretical and experimental methods.
The previous research results of the GFRP were reviewed and discussed firstly in this paper. Through comparing with the experimental data, the applicability of various models and their ability of dealing with practical problems were presented.
Six kinds of GFRP laminates, 162 specimens totally, were tested in this research. Among of them, 50 specimens were tested for static strength and 112 for fatigue life, depending on which, the comprehensive fatigue behavior and fatigue life data of GFRP were obtained. The normalized stiffness degradation curves were provided for the same laminate under different ratio of stress to its strength and different laminates under same ratio of stress to individual strength. The reason why the stiffness is decreasing along with the cycles was given through the evolution of microcosmic damages in the material. Based on the comprehensive experimental research on the GFRP’s fatigue behavior, the theoretical research was carried out as follows: Based on the definition of a condition function for the GFRP under axial loading, a theoretical model was presented to predict the S-N curve of off-axis unidirectional laminate with arbitrary angle by the S-N curves of 0o and 90o laminate; Considering the fatigue damage mechanism of GFRP laminates, a fatigue life model was presented to predict the S-N curve of arbitrary laminate with complex stacking sequence by the S-N curves of 0o and 90o laminate; A stiffness degradation model was proposed, and was proved to describe the degradation rules well.
Through comparing the theoretical models with the experimental results, it shows that the predicting results of these theoretical models agree well with the experiment results. The experimental results of this research can be applied in GFRP structure design and the models could be applied in GFRP structure’s fatigue analysis and life prediction.
论文首先回顾了纤维增强复合材料疲劳行为研究领域已经取得的研究成果,并对这些成果进行了分析和论述,通过实验数据的计算比较,给出了各种分析模型的适应性和解决实际问题的符合程度。
论文完成了6种层合板162个有效的玻璃纤维增强树脂基复合材料层合板试验件的测试,其中50个试件用于静强度测试,112个试件用于疲劳性能测试。获得了比较系统的玻璃纤维增强复合材料层合板的疲劳性能数据。给出了同种试件在不同的加载比下的刚度降曲线,以及不同种类试件在相同加载比下的刚度降曲线,并从材料内部微观损伤扩展机理的角度解释了刚度随损伤单调下降原因。在疲劳试验的基础上对玻璃纤维增强复合材料层合板的疲劳行为开展了理论研究:给出了定义玻璃纤维增强复合材料层合板在轴向应力作用下的状态函数,提出了一个由0°和90°单向板的S—N曲线来获得任意偏角层合板的S—N曲线的疲劳寿命模型;基于玻璃纤维增强复合材料层合板的疲劳破坏机理,提出了一个由0°和90°单向板的S—N曲线来获得任意铺层层合板S—N曲线的模型;提出了一个描述层合板刚度退化的模型,该模型可以很好地描述玻璃纤维增强复合材料层合板的刚度退化规律。
研究结果表明:论文中提出的理论分析模型和实验结果吻合的很好。本文所获得的实验结果可直接用于玻璃纤维增强树脂基复合材料结构的设计,所提出的理论分析模型可用于任意铺层的玻璃纤维增强复合材料层合板结构的分析计算。
Glass Fiber Reinforced Polymer (GFRP) has been widely used in the fields of aeronautics, automobile, shipping and civil industry. Although the fatigue problem of the GFRP were encountered everywhere, the fatigue mechanism could not be essentially described based on its fatigue phenomena, and there was no general method for the fatigue life’s prediction. In this paper, the fatigue behaviors of GFRP laminates were systematically researched by theoretical and experimental methods.
The previous research results of the GFRP were reviewed and discussed firstly in this paper. Through comparing with the experimental data, the applicability of various models and their ability of dealing with practical problems were presented.
Six kinds of GFRP laminates, 162 specimens totally, were tested in this research. Among of them, 50 specimens were tested for static strength and 112 for fatigue life, depending on which, the comprehensive fatigue behavior and fatigue life data of GFRP were obtained. The normalized stiffness degradation curves were provided for the same laminate under different ratio of stress to its strength and different laminates under same ratio of stress to individual strength. The reason why the stiffness is decreasing along with the cycles was given through the evolution of microcosmic damages in the material. Based on the comprehensive experimental research on the GFRP’s fatigue behavior, the theoretical research was carried out as follows: Based on the definition of a condition function for the GFRP under axial loading, a theoretical model was presented to predict the S-N curve of off-axis unidirectional laminate with arbitrary angle by the S-N curves of 0o and 90o laminate; Considering the fatigue damage mechanism of GFRP laminates, a fatigue life model was presented to predict the S-N curve of arbitrary laminate with complex stacking sequence by the S-N curves of 0o and 90o laminate; A stiffness degradation model was proposed, and was proved to describe the degradation rules well.
Through comparing the theoretical models with the experimental results, it shows that the predicting results of these theoretical models agree well with the experiment results. The experimental results of this research can be applied in GFRP structure design and the models could be applied in GFRP structure’s fatigue analysis and life prediction.
引文
[1]王虎.复合材料在飞机上的应用.玻璃钢/复合材料,1992(6):43-44.
[2]李成功,傅恒志,于翘,等.航空航天材料.北京:国防工业出版社,2002.
[3]王燕.先进复合材料在飞机上的应用.西飞科技,2001(3):45~46.
[4]沈观林,胡更开.复合材料力学.北京:清华大学出版社,2006.
[5]陈绍杰.复合材料与A380客机.航空制造技术,2002(9):27-29.
[6] Talreja R.Fatigue of composite material.1st,Lancaster, Pennsylvania:Technomic Publishing Company, Inc,1987.
[7] Talreja R. Fatigue Reliability under multiple amplitude loads. Engineering Fracture Mechanics, 1979, 11: 839-849.
[8] Talreja R. Fatigue of composite materials: Damage Mechanisms and Fatigue Life Diagrams. Proc. R. Soc. Lond. A378, 1981, 7: 461-475.
[9] Hashin Z, Rotem A. A fatigue failure criterion for fiber reinforced materials. Journal of Composite Materials, 1973,7(10):448-464.
[10] Rotem A, Hashin Z. Fatigue failure of angle ply laminates. AIAA Journal, 1976,14(7):868-872.
[11] Hashin Z. Cumulative damage theory for composite materials: Residual Life and Residual Strength Methods. Composites Science and Technology, 1985, 23: 1-19.
[12] Owen M J, Dukes R. Fatigue of glass reinforced plastics under single and repeated loads. Journal of Strain Analysis, 1967, 2(4): 272-279.
[13] Owen M J,Rose R G. Polyester flexibility versus fatigue behavior of RP. modern plastics. 1970, 47(11): 130-138.
[14] Hahn H T, Tsai S W. On the behavior of compostes laminates after initial failures. Journal of Composite Materials, 1974, 8: 288-305.
[15] Hahn H T, Tsai S W. Fatigue behavior of composite laminates. Journal of Composite Material, 1976, 10: 156-180.
[16] Hahn H T. Fatigue behavior and life prediciton of compisite laminates. In: Composite Materials: Testing and Design (Fifth Conference). ASTM STP 674,1979, 383-417.
[17] Tsai S W. Composite design. United States Airforce Materials Laboratory:1986.
[18] Reifsnider K L, Henneke E G., Stinchcomb W W,Duke J C. Damage mechanics and NDE of composite laminates. In: Mechanics of Composite Materials. Recent Advances, 1983, 399-420.
[19] Reifsnider K L, Jaminson R D. Fracture of fatigue-loaded composite laminates. Int. Journal of Fatigue, 1982, 4: 187-198.
[20] Subramanian S, Reifsnider K L, Stinchcomb W W. A cumulative damage model to predict the fatigue life of composite laminates including the effect of a fiber-matrix interphase. International Journal of Fatigue, 1995, 17(5): 343-351.
[21] Yang J N, Jones D L, Yang S H, Meskini A.A stiffness degradation model for graphite/epoxy laminates.Journal of Composite Materials,1990,24:753~769.
[22] Yang J N, Jones D L. Statistical fatigue of Graphite/Epoxy angle-ply laminates in shear. Journal of Composite Materials, 1978, 12: 371-389.
[23] Yang J N, Jones D L. Effect of load sequence on the statistical fatigue of composites. AIAA Journal, 1980, 18(12): 1525-1531.
[24] Yang J N, Lee L J, Sheu D Y. Modulus reduction and fatigue damage of matrix dominate composite laminates. Composites Structures, 1992, 21: 91-100.
[25] Yao W X, N Himmel . A new cumulative fatigue damage model for fiber-reinforced plastics.Composites Science and Technology, 2000,60:59~64.
[26]顾怡,姚卫星.疲劳加载下纤维复合材料的剩余强度.复合材料学报,1999,15(2):128-132.
[27]翟洪军.含缺口复合材料层合板疲劳刚度退化分析.南京:南京航空航天大学,2001.
[28]吴富强,姚卫星.一种复合材料层合板的S—N曲线模型.机械强度,2004,26: 127-129.
[29]胡伟峰.复合材料层合板刚度退化的系列单元失效模型。南京:南京航空航天大学硕士学位论文,2006.
[30]吴富强.纤维增强复合材料疲劳寿命预测研究.南京:南京航空航天大学硕士学位论文,2005.
[31]轩福贞,孙树勋,汤红卫,程德明.复合材料层板疲劳损伤的有效耗能分析法.复合材料学报,1997,14(3):115-124.
[32] Reifsnider K L. Damage and damage mechanics. In: Reifsnider K L Ed. Fatigue of Composite Materials, B V: Elsevier Science Publishers, 1990, 11-77.
[33] Poursartip A, Ashby M F,Beaumont P W R. The fatigue damage mechanics of a carbon fibre composite laminate: I-development of the model. Composites Science and Technology, 1986, 25:193-218.
[34] Fong J T. What is fatigue damage? In: Reifsnider K L Ed. Damage in Composite Materials. ASTM STP 775, 1982, 243-266.
[35] Otani N, Song D Y. Fatigue life prediction of composite under two-stage loading. Journal of Materials Science, 1997, 32:775-760.
[36] Han K S, Hwang W. Fatigue life prediction and failure mechanisms of composite materials. Advanced Composite Materials, 1992, 2(1):29-50.
[37] Ye L. On fatigue damage accumulation and material degradation in composite materials. Composites Science and Technology, 1989, 36:339-350.
[38] Matsuoka S. Relaxation phenomena in polymers. Hanser Publishers, 1992.
[39] Kubat J, Rigdahl M. Stress-relaxation behaviour of solid polymers. In: Brostow W and Corneliussen R D ed. Fatigue of Plastics. Hanser Publishers, 1986, 24-59.
[40] Yang J N. Fatigue and residual strength degradation for graphite/epoxy composites under tension-compression cyclic loadings. Journal Composite Materials, 1978, 12:19-39.
[41] Broutman L J, Sahu S. A new theory to predict cumulative fatigue damage in fiberglass reinforced plastics. Composite Materials: Testing and Design (2nd Conference), ASTM STP 497, 1972, 170-188.
[42] Donaldson S L, Kim R Y.Life prediction of glass/vinylester and glass/polyester composites under fatigue loading[A].Proceedings of the 10th International Conference on Composite Materials[C]. Fatigue and fracture.Woodhead Publishing Limited,1995, 1:557-584.
[43] Andersons J, Korsgaard J. Residual strength of GRP at high cycle fatigue. Proceedings of ICCM-11. 1997, II:135-144.
[44] Tai H, C. C. Ma M, Wu S H. Fatigue behaviour of carbon fibre/PEEK laminatecomposites. Composites, 1995, 26(8):551-559.
[45] Haque P A, Krishnagopalan J, Jeelani S. Fatigue damage in laminated composites. Journal of Reinforced Plastics and Composites, 1993, 12:1058-1069.
[46] Yang J N, Liu M D. Residual strength degradation model and theory of periodic proof tests for graphite/epoxy laminates. AFML-TR-76-225, Wright-Patterson AFB, 1976.
[47] Charewicz A, Daniel I M. Damage mechanisms and accumulation in graphite/epoxy laminates. In: Hahn H T Ed. Composite Materials. Fatigue and fracture . ASTM STP 907,1986,274-297.
[48] Chou P C, Croman R. Residual strength in fatigue based on the strength-life equal rank assumption. Journal of Composite Material, 1978, 12:177-194.
[49] Chou P C, Croman R. Degradation and sudden-death models of fatigue of graphite/epoxy composites. In: Composite Materials:Testing and Design(5th conference). ASTM STP 674, 1979, 431-454.
[50] Schaff J R,Davidson B D. Life prediction methodology for composite structures, Part I-Constant amplitude and two-stress level fatigue. Journal of Composite Materials, 1997, 31:128-157.
[51] Sendeckyj G. P. Life prediction for resin-matrix composite materials. In: Reifsnider K L Ed. Fatigue of composite materials. B V: Elsevier Science Publishers, 1990, 431-483.
[52] Jiang Y Q. The stiffness reduction of composite laminates due to fatigue damage. Proceedings of ICCM8, 1991, 38-C-(1-6).
[53] El Mahi A, Berthelot J M,Brillaud J. Stiffness reduction and energy release rate of cross-ply laminates during fatigue tests. Composite Structures, 1995, 30:123-130.
[54] Coats T W, Harris C E. Experimental verification of a progressive damage model for IM7/5260 laminates subjected to tension-tension fatigue. Journal of Composite Materials, 1995, 29(3): 280-305.
[55] Bangyan L, Lessard L B. Fatigue and damage-tolerance analysis of composite laminates: Stiffness loss, damage-modeling and life prediction. Composites Science and Technology, 1994, 51: 43-51.
[56] Lim S G.,Hong C S. Prediction of transverse cracking and stiffness reduction in cross-ply laminated composites. Journal of Composite Materials, 1989, 23:695-713.
[57] Highsmith A L, Reifsnider K L. Stiffness-reduction mechanisms in composite laminates. In: Reifsnider K L Ed. Damage in Composite Materials. ASTM STP 775, 1982, 103-117.
[58] Plumtree A, Shen G.. Prediction of fatigue damage development in unidirectional long fibre composites. Polymers and Polymer Composites, 1994, 2(2):83-90.
[59] Wu W F, Lee L J, Choi S T. A study of fatigue damage and fatigue life of composite laminates. Journal of Composite Materials, 1996, 30(1):123-137.
[60] Echtermeyer A T, Engh B, Buene L. Lifetime and Young’s modulus changes of glass/phenolic and glass/polyester composites under fatigue. Composites, 1995, 26(1):10-16.
[61] Zhang D Q,Sandor B I. Damage evaluation in composite materials using thermographic stress analysis. In: Mitchell M R and Landgraf R W Eds. Advances in Fatigue Lifetime Predictive Techniques. ASTM STP 1122, 1992, 341-353.
[62] Whitworth H A. Modeling stiffness reduction of graphite/epoxy composite laminates. Journal of Composite Materials, 1987, 21:362-372.
[63] Hwang W, Han K S. Fatigue of composite, fatigue modulus concept and life prediction. Journal of Composite Materials, 1986, 20:155-165.
[64]韩京燮,黄云峰.复合材料疲劳寿命的预测.复合材料学报, 1987, 4(1):16-24.
[65] Philippidis T P,Vassilopoulos A P. Fatigue of composite laminates under off-axis loading. International Journal of Fatigue, 1999, 22(3):253-262.
[66] Kawakami H, Fujii T J, Morita Y. Fatigue degradation and life prediction of glass fabric polymer composite under tension/torsion biaxial loadings. Journal of Reinforced Plastics and Composites, 1996, 15:183-195.
[67] O’Brien T K,Reifsnider K L. Fatigue damage evaluation through stiffness measurements in boron-epoxy laminates. Journal of Composite Materials, 1981, 15:55-70.
[68] Dvorak G. J, Laws N, Hejazi M. Analysis of progressive matrix cracking in composite laminates, 1. Thermoelastic properties of a ply with cracks. Journal of Composite Materials, 1985, 19(3):216-234.
[69] Talreja R. Transverse cracking and stiffness reduction in composite laminates. Journal of Composite Materials, 1985, 19(4):355-375.
[70] Groves S E, Harris C H, Highsmith A L, Allen D H,Norvell R G.. An experimental and analytical treatment of matrix cracking in cross-ply laminate. Experimental Mechanics, 1987, 27(1):73-79.
[71] Renard J, Favre J P, Jeggy Th. Influence of transverse cracking on ply behaviour: Introduction of a characteristic damage variable. Composites Science and Technology, 1993, 46:29-37.
[72]姚卫星. Miner理论的统计特性分析.航空学报,1995, 16(5):601-604.
[73] Hashin Z, Rotem A. A cumulative damage theory of fatigue failure. Materials Science and Engineering, 1978, 34:146-160.
[74] Poursartip A, Beaumont P W R. The fatigue damage mechanics of a carbon fiber composite laminate: II-life prediction. Composites Science and technology, 1986, 25:283-299.
[75] Bogdanoff J L. A new cumulative damage model: Part 1. Journal of Applied Mechanics, 1978, 45:246-250.
[76] Bogdanoff J L, Krieger W. A new cumulative damage model: Part 2. Journal of Applied Mechanics, 1978, 45:251-257.
[77] Ganesan R, Hoa S V, Zhang S,El-Karmalawy M. A stochastic cumulative damage model for the fatigue response of laminated composites. Proceedings of ICCM-11, 1997,Ⅱ145-Ⅱ156.
[78] Mandell F, Urs Meier. Fatigue crack propagation in 00/900 E-glass/epoxy composites. In: Fatigue of Composite Materials. ASTM STP569, 1975, 28-44.
[79] Adam T, Gathercole N, Reiter H,Harris B. Life prediction for fatigue of T800/5245 carbon-fibre composites, II. variable-amplitude loading. International Journal of Fatigue, 1994, 16:533-547.
[80] Gathercole N, Reiter H, Adam T, Harris B. Life prediction for fatigue of T800/5245 carbon-fibre composites, I. constant-amplitude loading. International Journal of Fatigue, 1994, 16:523-523.
[81] Harris B, Gathercole N, Reiter H, Adam T. Fatigue of carbon-fibre-reinforced plastics under block loading conditions. Composites Part A, 1997, 28A:327-337.
[82] Hwang W, Han K S.Fatigue of composite materials damage model and life prediction[A].Composite Materials Fatigue and fracture[C].ASTM STP 1012, 1989, 87-102.
[83] Kadi H E, Ellyin F.Effect of stress ratio on the fatigue of unidirectional glass fibre/epoxy composite laminae[J].Composites,1994, 25(10):917-924.
[84] Sims D F, Brogdon V H.Fatigue behavior of composites under different loading modes[A].In: Reifsnider KL, Lauraitis KN, Ed. Fatigue of Filamentary Composite Materials[C]. ASTM STP 636, 1977, 185-205.
[85] Awerbuch Jonathan, Hahn H T . Off-axis fatigue of graphite/epoxy composite[A].Fatigue of Fibrous Composite Materials[C], ASTM STP 723, 1981, 243-273.
[86] Jen M H R, Lee C H.Strength and life in thermoplastic composite laminates under stastic and fatigue loads. Part II: formulation.International Journal of Fatigue, 1998, 20(9): 617-629.
[87] Plumtree A, Cheng G X.A fatigue damage parameter for off-axis unidirectional fibre-reinforced composites.International Journal of Fatigue.1999, 21: 849-856.
[88] Kawai M . A phenomenological model for off-axis fatigue behavior of unidirectional polymer matrix composites under different stress ratios.Composite Part A, 2004, 35: 955-963.
[89] Shokrieh M M, Taheri-Behrooz F.A unified fatigue life model based on energy method.Composite Structures, 2006, 75: 444-450.
[90] Varvani-Farahani A, Haftchenari H, Panbechi M.A fatigue damage parameter for life assessment of off-axis unidirectional GRP composites.Journal of Composite Materials, 2006, 40(18): 1659-1670.
[91] Salekeen S, Jones D L. Fatigue response of thick section fiberglass/epoxy composites. Composite Structures, 2007,79:119-124.
[92] Gagel A, Fiedler B, Schulte K. On modeling the mechanical degradation of fatigue loaded glass-fibre non-crimp fabric reinforced epoxy laminates.Composites Science and Technology, 2006, 66: 657-664.
[93] Petermann J, Schulte K. Strain based service time estimation for angle-ply laminates. Composite Science and Technology, 2002, 62:1043-1050.
[94] Pandita S D, Verpoest I. Tension-tension fatigue behavior of knitted fabric composites. Composite Structures, 2004, 64: 199-209.
[95] Whitworth H A. A stiffness degradation model for composite laminates under fatigue loading. Composite Structures, 1998, 40(2): 95-101.
[96] Joffe R, Krasnikovs A, Varna J. COD-Based simulation of transverse cracking and stiffness reduction in [S/90n]S laminates. Composites science and Technology, 2001, 61:637-656.
[97] Brillaud J, El Mahi A. Numerical simulation of the influence of stacking sequence on transverse ply cracking in composite laminates. Composite Structures, 1991, 17:23-35.
[98] Zhang H, Minnctyan L. Variational analysis of transverse cracking and local delamination in [0m/90n]S laminates. International Journal of Solids and Structures. 2006.
[99] Kashtalyan M, Soutis C. The effect of delaminations induced by transverse cracks and splits on stiffness properties of composite laminates. Composites Part A: Applied Science and Manufacturing. 2000, 31:107-119.
[100] Gamstedt E K, Berglund L A, Peijs T. Fatigue mechanisms in unidirectional glass-fibre-reinforced polypropylene. Composite Science and Technology, 1999, 59: 759-768.
[2]李成功,傅恒志,于翘,等.航空航天材料.北京:国防工业出版社,2002.
[3]王燕.先进复合材料在飞机上的应用.西飞科技,2001(3):45~46.
[4]沈观林,胡更开.复合材料力学.北京:清华大学出版社,2006.
[5]陈绍杰.复合材料与A380客机.航空制造技术,2002(9):27-29.
[6] Talreja R.Fatigue of composite material.1st,Lancaster, Pennsylvania:Technomic Publishing Company, Inc,1987.
[7] Talreja R. Fatigue Reliability under multiple amplitude loads. Engineering Fracture Mechanics, 1979, 11: 839-849.
[8] Talreja R. Fatigue of composite materials: Damage Mechanisms and Fatigue Life Diagrams. Proc. R. Soc. Lond. A378, 1981, 7: 461-475.
[9] Hashin Z, Rotem A. A fatigue failure criterion for fiber reinforced materials. Journal of Composite Materials, 1973,7(10):448-464.
[10] Rotem A, Hashin Z. Fatigue failure of angle ply laminates. AIAA Journal, 1976,14(7):868-872.
[11] Hashin Z. Cumulative damage theory for composite materials: Residual Life and Residual Strength Methods. Composites Science and Technology, 1985, 23: 1-19.
[12] Owen M J, Dukes R. Fatigue of glass reinforced plastics under single and repeated loads. Journal of Strain Analysis, 1967, 2(4): 272-279.
[13] Owen M J,Rose R G. Polyester flexibility versus fatigue behavior of RP. modern plastics. 1970, 47(11): 130-138.
[14] Hahn H T, Tsai S W. On the behavior of compostes laminates after initial failures. Journal of Composite Materials, 1974, 8: 288-305.
[15] Hahn H T, Tsai S W. Fatigue behavior of composite laminates. Journal of Composite Material, 1976, 10: 156-180.
[16] Hahn H T. Fatigue behavior and life prediciton of compisite laminates. In: Composite Materials: Testing and Design (Fifth Conference). ASTM STP 674,1979, 383-417.
[17] Tsai S W. Composite design. United States Airforce Materials Laboratory:1986.
[18] Reifsnider K L, Henneke E G., Stinchcomb W W,Duke J C. Damage mechanics and NDE of composite laminates. In: Mechanics of Composite Materials. Recent Advances, 1983, 399-420.
[19] Reifsnider K L, Jaminson R D. Fracture of fatigue-loaded composite laminates. Int. Journal of Fatigue, 1982, 4: 187-198.
[20] Subramanian S, Reifsnider K L, Stinchcomb W W. A cumulative damage model to predict the fatigue life of composite laminates including the effect of a fiber-matrix interphase. International Journal of Fatigue, 1995, 17(5): 343-351.
[21] Yang J N, Jones D L, Yang S H, Meskini A.A stiffness degradation model for graphite/epoxy laminates.Journal of Composite Materials,1990,24:753~769.
[22] Yang J N, Jones D L. Statistical fatigue of Graphite/Epoxy angle-ply laminates in shear. Journal of Composite Materials, 1978, 12: 371-389.
[23] Yang J N, Jones D L. Effect of load sequence on the statistical fatigue of composites. AIAA Journal, 1980, 18(12): 1525-1531.
[24] Yang J N, Lee L J, Sheu D Y. Modulus reduction and fatigue damage of matrix dominate composite laminates. Composites Structures, 1992, 21: 91-100.
[25] Yao W X, N Himmel . A new cumulative fatigue damage model for fiber-reinforced plastics.Composites Science and Technology, 2000,60:59~64.
[26]顾怡,姚卫星.疲劳加载下纤维复合材料的剩余强度.复合材料学报,1999,15(2):128-132.
[27]翟洪军.含缺口复合材料层合板疲劳刚度退化分析.南京:南京航空航天大学,2001.
[28]吴富强,姚卫星.一种复合材料层合板的S—N曲线模型.机械强度,2004,26: 127-129.
[29]胡伟峰.复合材料层合板刚度退化的系列单元失效模型。南京:南京航空航天大学硕士学位论文,2006.
[30]吴富强.纤维增强复合材料疲劳寿命预测研究.南京:南京航空航天大学硕士学位论文,2005.
[31]轩福贞,孙树勋,汤红卫,程德明.复合材料层板疲劳损伤的有效耗能分析法.复合材料学报,1997,14(3):115-124.
[32] Reifsnider K L. Damage and damage mechanics. In: Reifsnider K L Ed. Fatigue of Composite Materials, B V: Elsevier Science Publishers, 1990, 11-77.
[33] Poursartip A, Ashby M F,Beaumont P W R. The fatigue damage mechanics of a carbon fibre composite laminate: I-development of the model. Composites Science and Technology, 1986, 25:193-218.
[34] Fong J T. What is fatigue damage? In: Reifsnider K L Ed. Damage in Composite Materials. ASTM STP 775, 1982, 243-266.
[35] Otani N, Song D Y. Fatigue life prediction of composite under two-stage loading. Journal of Materials Science, 1997, 32:775-760.
[36] Han K S, Hwang W. Fatigue life prediction and failure mechanisms of composite materials. Advanced Composite Materials, 1992, 2(1):29-50.
[37] Ye L. On fatigue damage accumulation and material degradation in composite materials. Composites Science and Technology, 1989, 36:339-350.
[38] Matsuoka S. Relaxation phenomena in polymers. Hanser Publishers, 1992.
[39] Kubat J, Rigdahl M. Stress-relaxation behaviour of solid polymers. In: Brostow W and Corneliussen R D ed. Fatigue of Plastics. Hanser Publishers, 1986, 24-59.
[40] Yang J N. Fatigue and residual strength degradation for graphite/epoxy composites under tension-compression cyclic loadings. Journal Composite Materials, 1978, 12:19-39.
[41] Broutman L J, Sahu S. A new theory to predict cumulative fatigue damage in fiberglass reinforced plastics. Composite Materials: Testing and Design (2nd Conference), ASTM STP 497, 1972, 170-188.
[42] Donaldson S L, Kim R Y.Life prediction of glass/vinylester and glass/polyester composites under fatigue loading[A].Proceedings of the 10th International Conference on Composite Materials[C]. Fatigue and fracture.Woodhead Publishing Limited,1995, 1:557-584.
[43] Andersons J, Korsgaard J. Residual strength of GRP at high cycle fatigue. Proceedings of ICCM-11. 1997, II:135-144.
[44] Tai H, C. C. Ma M, Wu S H. Fatigue behaviour of carbon fibre/PEEK laminatecomposites. Composites, 1995, 26(8):551-559.
[45] Haque P A, Krishnagopalan J, Jeelani S. Fatigue damage in laminated composites. Journal of Reinforced Plastics and Composites, 1993, 12:1058-1069.
[46] Yang J N, Liu M D. Residual strength degradation model and theory of periodic proof tests for graphite/epoxy laminates. AFML-TR-76-225, Wright-Patterson AFB, 1976.
[47] Charewicz A, Daniel I M. Damage mechanisms and accumulation in graphite/epoxy laminates. In: Hahn H T Ed. Composite Materials. Fatigue and fracture . ASTM STP 907,1986,274-297.
[48] Chou P C, Croman R. Residual strength in fatigue based on the strength-life equal rank assumption. Journal of Composite Material, 1978, 12:177-194.
[49] Chou P C, Croman R. Degradation and sudden-death models of fatigue of graphite/epoxy composites. In: Composite Materials:Testing and Design(5th conference). ASTM STP 674, 1979, 431-454.
[50] Schaff J R,Davidson B D. Life prediction methodology for composite structures, Part I-Constant amplitude and two-stress level fatigue. Journal of Composite Materials, 1997, 31:128-157.
[51] Sendeckyj G. P. Life prediction for resin-matrix composite materials. In: Reifsnider K L Ed. Fatigue of composite materials. B V: Elsevier Science Publishers, 1990, 431-483.
[52] Jiang Y Q. The stiffness reduction of composite laminates due to fatigue damage. Proceedings of ICCM8, 1991, 38-C-(1-6).
[53] El Mahi A, Berthelot J M,Brillaud J. Stiffness reduction and energy release rate of cross-ply laminates during fatigue tests. Composite Structures, 1995, 30:123-130.
[54] Coats T W, Harris C E. Experimental verification of a progressive damage model for IM7/5260 laminates subjected to tension-tension fatigue. Journal of Composite Materials, 1995, 29(3): 280-305.
[55] Bangyan L, Lessard L B. Fatigue and damage-tolerance analysis of composite laminates: Stiffness loss, damage-modeling and life prediction. Composites Science and Technology, 1994, 51: 43-51.
[56] Lim S G.,Hong C S. Prediction of transverse cracking and stiffness reduction in cross-ply laminated composites. Journal of Composite Materials, 1989, 23:695-713.
[57] Highsmith A L, Reifsnider K L. Stiffness-reduction mechanisms in composite laminates. In: Reifsnider K L Ed. Damage in Composite Materials. ASTM STP 775, 1982, 103-117.
[58] Plumtree A, Shen G.. Prediction of fatigue damage development in unidirectional long fibre composites. Polymers and Polymer Composites, 1994, 2(2):83-90.
[59] Wu W F, Lee L J, Choi S T. A study of fatigue damage and fatigue life of composite laminates. Journal of Composite Materials, 1996, 30(1):123-137.
[60] Echtermeyer A T, Engh B, Buene L. Lifetime and Young’s modulus changes of glass/phenolic and glass/polyester composites under fatigue. Composites, 1995, 26(1):10-16.
[61] Zhang D Q,Sandor B I. Damage evaluation in composite materials using thermographic stress analysis. In: Mitchell M R and Landgraf R W Eds. Advances in Fatigue Lifetime Predictive Techniques. ASTM STP 1122, 1992, 341-353.
[62] Whitworth H A. Modeling stiffness reduction of graphite/epoxy composite laminates. Journal of Composite Materials, 1987, 21:362-372.
[63] Hwang W, Han K S. Fatigue of composite, fatigue modulus concept and life prediction. Journal of Composite Materials, 1986, 20:155-165.
[64]韩京燮,黄云峰.复合材料疲劳寿命的预测.复合材料学报, 1987, 4(1):16-24.
[65] Philippidis T P,Vassilopoulos A P. Fatigue of composite laminates under off-axis loading. International Journal of Fatigue, 1999, 22(3):253-262.
[66] Kawakami H, Fujii T J, Morita Y. Fatigue degradation and life prediction of glass fabric polymer composite under tension/torsion biaxial loadings. Journal of Reinforced Plastics and Composites, 1996, 15:183-195.
[67] O’Brien T K,Reifsnider K L. Fatigue damage evaluation through stiffness measurements in boron-epoxy laminates. Journal of Composite Materials, 1981, 15:55-70.
[68] Dvorak G. J, Laws N, Hejazi M. Analysis of progressive matrix cracking in composite laminates, 1. Thermoelastic properties of a ply with cracks. Journal of Composite Materials, 1985, 19(3):216-234.
[69] Talreja R. Transverse cracking and stiffness reduction in composite laminates. Journal of Composite Materials, 1985, 19(4):355-375.
[70] Groves S E, Harris C H, Highsmith A L, Allen D H,Norvell R G.. An experimental and analytical treatment of matrix cracking in cross-ply laminate. Experimental Mechanics, 1987, 27(1):73-79.
[71] Renard J, Favre J P, Jeggy Th. Influence of transverse cracking on ply behaviour: Introduction of a characteristic damage variable. Composites Science and Technology, 1993, 46:29-37.
[72]姚卫星. Miner理论的统计特性分析.航空学报,1995, 16(5):601-604.
[73] Hashin Z, Rotem A. A cumulative damage theory of fatigue failure. Materials Science and Engineering, 1978, 34:146-160.
[74] Poursartip A, Beaumont P W R. The fatigue damage mechanics of a carbon fiber composite laminate: II-life prediction. Composites Science and technology, 1986, 25:283-299.
[75] Bogdanoff J L. A new cumulative damage model: Part 1. Journal of Applied Mechanics, 1978, 45:246-250.
[76] Bogdanoff J L, Krieger W. A new cumulative damage model: Part 2. Journal of Applied Mechanics, 1978, 45:251-257.
[77] Ganesan R, Hoa S V, Zhang S,El-Karmalawy M. A stochastic cumulative damage model for the fatigue response of laminated composites. Proceedings of ICCM-11, 1997,Ⅱ145-Ⅱ156.
[78] Mandell F, Urs Meier. Fatigue crack propagation in 00/900 E-glass/epoxy composites. In: Fatigue of Composite Materials. ASTM STP569, 1975, 28-44.
[79] Adam T, Gathercole N, Reiter H,Harris B. Life prediction for fatigue of T800/5245 carbon-fibre composites, II. variable-amplitude loading. International Journal of Fatigue, 1994, 16:533-547.
[80] Gathercole N, Reiter H, Adam T, Harris B. Life prediction for fatigue of T800/5245 carbon-fibre composites, I. constant-amplitude loading. International Journal of Fatigue, 1994, 16:523-523.
[81] Harris B, Gathercole N, Reiter H, Adam T. Fatigue of carbon-fibre-reinforced plastics under block loading conditions. Composites Part A, 1997, 28A:327-337.
[82] Hwang W, Han K S.Fatigue of composite materials damage model and life prediction[A].Composite Materials Fatigue and fracture[C].ASTM STP 1012, 1989, 87-102.
[83] Kadi H E, Ellyin F.Effect of stress ratio on the fatigue of unidirectional glass fibre/epoxy composite laminae[J].Composites,1994, 25(10):917-924.
[84] Sims D F, Brogdon V H.Fatigue behavior of composites under different loading modes[A].In: Reifsnider KL, Lauraitis KN, Ed. Fatigue of Filamentary Composite Materials[C]. ASTM STP 636, 1977, 185-205.
[85] Awerbuch Jonathan, Hahn H T . Off-axis fatigue of graphite/epoxy composite[A].Fatigue of Fibrous Composite Materials[C], ASTM STP 723, 1981, 243-273.
[86] Jen M H R, Lee C H.Strength and life in thermoplastic composite laminates under stastic and fatigue loads. Part II: formulation.International Journal of Fatigue, 1998, 20(9): 617-629.
[87] Plumtree A, Cheng G X.A fatigue damage parameter for off-axis unidirectional fibre-reinforced composites.International Journal of Fatigue.1999, 21: 849-856.
[88] Kawai M . A phenomenological model for off-axis fatigue behavior of unidirectional polymer matrix composites under different stress ratios.Composite Part A, 2004, 35: 955-963.
[89] Shokrieh M M, Taheri-Behrooz F.A unified fatigue life model based on energy method.Composite Structures, 2006, 75: 444-450.
[90] Varvani-Farahani A, Haftchenari H, Panbechi M.A fatigue damage parameter for life assessment of off-axis unidirectional GRP composites.Journal of Composite Materials, 2006, 40(18): 1659-1670.
[91] Salekeen S, Jones D L. Fatigue response of thick section fiberglass/epoxy composites. Composite Structures, 2007,79:119-124.
[92] Gagel A, Fiedler B, Schulte K. On modeling the mechanical degradation of fatigue loaded glass-fibre non-crimp fabric reinforced epoxy laminates.Composites Science and Technology, 2006, 66: 657-664.
[93] Petermann J, Schulte K. Strain based service time estimation for angle-ply laminates. Composite Science and Technology, 2002, 62:1043-1050.
[94] Pandita S D, Verpoest I. Tension-tension fatigue behavior of knitted fabric composites. Composite Structures, 2004, 64: 199-209.
[95] Whitworth H A. A stiffness degradation model for composite laminates under fatigue loading. Composite Structures, 1998, 40(2): 95-101.
[96] Joffe R, Krasnikovs A, Varna J. COD-Based simulation of transverse cracking and stiffness reduction in [S/90n]S laminates. Composites science and Technology, 2001, 61:637-656.
[97] Brillaud J, El Mahi A. Numerical simulation of the influence of stacking sequence on transverse ply cracking in composite laminates. Composite Structures, 1991, 17:23-35.
[98] Zhang H, Minnctyan L. Variational analysis of transverse cracking and local delamination in [0m/90n]S laminates. International Journal of Solids and Structures. 2006.
[99] Kashtalyan M, Soutis C. The effect of delaminations induced by transverse cracks and splits on stiffness properties of composite laminates. Composites Part A: Applied Science and Manufacturing. 2000, 31:107-119.
[100] Gamstedt E K, Berglund L A, Peijs T. Fatigue mechanisms in unidirectional glass-fibre-reinforced polypropylene. Composite Science and Technology, 1999, 59: 759-768.